for the question "Should I buy a traditional wood fired oven or a portable pizza oven?" there is no straight and easy answer!... and if you ask why, I'll say - Because! :) ...
I would need to know more, like,
the purpose you have for the wood fired oven
what space you have to install the wood fired oven
what's your budget for the oven
1st, they are completely different in the way they are built. Normaly, the portable pizza oven is made in stainless steel, ceramics and a fire brick is alot lighter than the traditional brick oven, that is made with clay and refractory bricks, making it alot heavier.
2nd, the traditional oven made of clay and bricks takes alot longer to heatup but then it also maintains the temperature for alot longer